Some of this thread has gotten rather wildly speculative, as one might perhaps expect from the topic. Still, there are serious papers about time travel in the physics literature.
In an attempt to get the thread "back on track", I'm going to quote some semi-popular and more professional papers about time travel in the context of General Relativity to try and give interested readers a feeling for the current state of the physics in this frontier area as it is actually written about by the physics community.
John Cramer's "Alternate view" column is written by a physicist, and tends to stick reasonably closely to the facts (Cramer is a physicist himself).
http://www.npl.washington.edu/AV/altvw33.html is, for instance, a discussion of one of the main ways that time travel might be possible in GR, through wormholes. A collection of Cramer's alternate view columns is online, and is a good place to start looking for semi-popular accounts about time travel.
Kip Thorne's book: "Wormholes and time machines: Einstein's outrageous legacy" is another good readable popularization which covers this material.
Now, for some of the published papers (published papers are the best way to understand the topic, but the most work - that's why I opened the thread with some of the better popular media discussions which stick close to the facts.)
http://prola.aps.org/abstract/PRL/v61/i13/p1446_1 is Moris and Thorne's famous paper. The abstract reads:
It is argued that, if the laws of physics permit an advanced civilization to create and maintain a wormhole in space for interstellar travel, then that wormhole can be converted into a time machine with which causality might be violatable. Whether wormholes can be created and maintained entails deep, ill-understood issues about cosmic censorship, quantum gravity, and quantum field theory, including the question of whether field theory enforces an averaged version of the weak energy condition.
This is still a good summary today though the paper is one of the earliest in the field and there have been many developments since then.
http://prola.aps.org/abstract/PRD/v46/i2/p603_1 Hawking's original "chronology protection" paper.
It has been suggested that an advanced civilization might have the technology to warp spacetime so that closed timelike curves would appear, allowing travel into the past. This paper examines this possibility in the case that the causality violations appear in a finite region of spacetime without curvature singularities. There will be a Cauchy horizon that is compactly generated and that in general contains one or more closed null geodesics which will be incomplete. One can define geometrical quantities that measure the Lorentz boost and area increase on going round these closed null geodesics. If the causality violation developed from a noncompact initial surface, the averaged weak energy condition must be violated on the Cauchy horizon. This shows that one cannot create closed timelike curves with finite lengths of cosmic string. Even if violations of the weak energy condition are allowed by quantum theory, the expectation value of the energy-momentum tensor would get very large if timelike curves become almost closed. It seems the back reaction would prevent closed timelike curves from appearing. These results strongly support the chronology protection conjecture: The laws of physics do not allow the appearance of closed timelike curves.
Note that chronology protection is still a conjecture, not a fact, but some particular classes of time machines have been disproved by Hawking's paper, such as:
http://prola.aps.org/abstract/PRD/v9/i8/p2203_1 Tipler's time machine. One of the earlier papers about time machine, this machine has been shown not to work unless the rotating cylinder is actually infinite by Hawking's paper above. This means it can't be built.
Gott's time machine with cosmic strings is another example of a historical time machine proposal which has fallen by the wayside due to Hawking's paper.
http://arxiv.org/abs/gr-qc/9703024 Some debate about the chronology protection postulate. One can probably find many more in this vein, this particular example was taken from the Wikipedia (and checked to make sure it was published).
http://adsabs.harvard.edu/abs/1993PhRvD..47.1432M talks about the "Grandfather paradox" of time travel using billiard balls
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRLTAO000095000002021101000001&idtype=cvips&gifs=yes
Ori's time machine proposal, which is one of the few non-wormhole time machines that gets around Hawking theorem. (I don't really understand the details, though, and I suspect many other readers will be in the same boat. It's still of some interest, though).
One can find also information on Mallet's time machine, in the media and in past threads. I'm not going to link to it because I personally believe Mallet's proposal is flawed - basically I think it falls afoul of Hawking's theorem, and other authors have published critical papers about it (see the past threads).
Mallet doesn't seem to agree with his critics (but I agree with the critics and disagree with Mallet).
There is probably more, but this should be enough reading to get people started in the right direction and away from some of the more overheated media speculation.
